Adaptive gps and ins integration system

ABSTRACT

This invention relates to the field of Inertial Navigation Systems (INS) and satellite navigation systems such as the Global Positioning System (GPS) and in particular relates to methods of integrating GPS and INS data in order to provide more accurate navigation solutions. The invention provides a method of improving the accuracy of a tightly coupled integrated INS and satellite radio navigation system in cases where the satellite navigation receiver has adaptive tracking loop bandwidths.

[0001] This invention relates to the field of Inertiai NavigationSystems (INS) and satellite positioning systems such as the GlobalPositioning System (GPS). In particular, this invention relates tomethods of integrating INS and GPS data in order to provide moreaccurate navigation solutions.

[0002] An INS comprises a set of accelerometers and gyroscopes, known asan inertial measurement unit (IMU), together with a navigation equationsprocessor, which integrates the IMU outputs to give the position,velocity and attitude. GPS consists of a constellation of satelliteswhich transmit navigation data to a GPS receiver. User location can bederived from the signals received from four separate satellites.Together, INS and GPS form the core navigation systems of militaryaircraft and missiles. Note: although the term “GPS” is used throughoutthe skilled man will appreciate that the invention relates to anysatellite navigation system that works along similar principles to GPS,e.g. Galileo. References to GPS should therefore be taken as meaning anysatellite system that operates in a GPS-like manner.

[0003] Integrating INS and GPS together provides a navigation solutionwhich combines the long term accuracy of GPS with the continuity, highbandwidth and low noise of INS.

[0004] There are four basic types of INS/GPS integration technique. Anuncoupled system simply uses the GPS data to periodically reset the INS.This approach is crude and, hence, is rarely used A loosely-coupledsystem compares the GPS navigation solution to that of the INS toestimate errors in both systems using a Kalman filter based algorithm(for more information on the Kalman filter algorithm see Applied OptimalEstimation by The Technical Staff of the Analytical SciencesCorporation, editor A GeIb, Massachusetts Institute of Technology Press(1974)). A tightly-coupled system, is similar to the loosely-coupledsystem but uses the range and range rate data transmitted from eachsatellite tracked instead of the GPS navigation solution. Finally, adeep integration system combines the GPS receiver tracking functions andINS/GPS integration within a common Kalman filter. This requires theredesign of, amongst other things, the GPS receiver, which requiresaccess to the GPS Receiver Applications Module (GRAM), which isrestricted by the US Government. Processor loads in a deep integrationsystem are also high and so this system has a number of drawbacks.

[0005] Both loosely-coupled and tightly-coupled systems are in commonuse. However, tightly coupled systems are more accurate and stable andare the subject of this invention (for further information on GPS/INSintegration see GPS/INS Integration, AGARD Lecture Series LS-207;Systems Implications and Innovative Applications of Satellite Navigationby R E Phillips and G T Schmidt).

[0006] Each navigation satellite transmits carrier signals on twofrequencies, known as L1 and L2, each with a pseudo-random codemodulated onto it. The GPS receiver will track the code and carriercomponents of each signal independently. Each receiver will thereforemaintain two so-called tracking loops for each satellite signal. Rangedata (referred to as “pseudo-range” in GPS terminology) is derived fromthe code signal tracking loop and range-rate data (referred to as“pseudo-range rate”) is derived from the carrier signal tracking loop.In normal GPS operation, each carrier tracking loop is used to aid thecorresponding code tracking loops. However, carrier tracking loops aremore sensitive to interference and will lose lock at lower interferencelevels than code tracking loops. The position of the receiver can bederived from the pseudo-range information and the velocity of thereceiver can be derived from the pseudo-range rate information.

[0007] The responsiveness of a GPS receiver is affected by noise (e.g.from interference with the GPS signal) and also by high dynamic vehiclemanoeuvres. The bandwidth of the tracking loops is a measure of thefrequency with which the receiver outputs independent range and rangerate measurements. High bandwidths enable a receiver to track thereceiver location more quickly whereas low bandwidths provide greaterresistance to interference. It is thus important to select bandwidthscarefully in order to maintain satisfactory receiver performance.

[0008] In the military environment many GPS receivers are capable ofadapting their tracking loop bandwidths in order to respond to changesin the level of vehicle motion and interference.

[0009] In an integrated INS/GPS (tightly coupled) system thepseudo-range and pseudo-range rate data from the GPS tracking loops areused as measurement inputs to a Kalman filter. In dual frequencyreceivers, the outputs from the L1 and L2 tracking channels are combinedprior to input to the Kalman filter in order to correct for ionospherepropagation delays. A reversionary mode is usually implemented wherebyINS data aids the code tracking loop in the event that the carriertracking loop loses lock and the GPS receiver is unable to deriverange-rate data.

[0010] The Kahnan filter is an estimation technique which provides anestimate of the GPS/INS system errors. Part of the Kalman filtertechnique is the calculation of the so-called Kalman gain matrix (K_(k))which relates the accuracy of the current measurement to that of theprevious estimates of the system errors. In order to correctly calculatethe measurement errors in the system the Kalman filter assumes that allmeasurements have time uncorrelated measurement errors. GeIb defines theKalman gain matrix (K_(k)) as K_(k)=P_(k)(−)H_(k)^(T)[H_(k)P_(k)(−)H_(k) ^(T)+R_(k)]⁻¹ where H_(k) is the measurementmatrix, R_(k) is the measurement noise covariance and [ ]⁻¹ denotes theinverse of the matrix.

[0011] In fact the errors in successive pseudo-range and pseudorange-rate data are correlated with correlation times inverselyproportional to the tracking loop bandwidths. If this fact is notaddressed then the Kalman filter becomes unstable, resulting in degradedestimates. Where the Kalman filter corrected INS data is used to aid GPScode tracking, a form of positive feedback can occur which eventuallycauses the GPS receiver to lose its tracking locks. The navigationsolution cannot be resurrected from the INS data alone, where thecorrected INS data is used to aid GPS, either because there is no standalone INS solution or because the INS solution, if available, is notaccurate enough. Therefore, where GPS receivers that do not haveadaptive bandwidths are used, this problem is circumvented by ensuringthat the Kalman filter updates its estimate of the measurement errors atan interval which is greater than the tracking loop measurementcorrelation time (of the order of 1 second), i.e. the interval betweeniterations of the Kalman filter measurement update phase is chosen to begreater than the tracking loop measurement correlation time. Sincedifferent receivers use different tracking loop bandwidths it isimportant that the INS/GPS integration Kalman filter is correctly tunedto the appropriate tracking loop bandwidths.

[0012] In cases where the receiver has adaptive tracking loop bandwidthstuning of the integration algorithm becomes more difficult. A commonapproach is to tune the algorithm to a relatively high bandwidth leveland disable the Kalman filter measurement inputs when the tracking loopbandwidth drops below a threshold value. This is obviously not an idealsolution since measurement data is being discarded which will inevitablyresult in a less than optimum navigation solution.

[0013] It is therefore an object of the present invention to provide amethod of improving the accuracy of a tightly coupled integrated INS andsatellite radio navigation system and to alleviate the above mentionedproblems.

[0014] Accordingly this invention provides a method of integratinginertial navigation system and satellite navigation system data in atightly coupled architecture by means of a Kalman filter, the satellitenavigation data being received on a receiver having adaptive trackingloop bandwidths, comprising

[0015] i) monitoring the tracking loop bandwidths or modelling them as afunction of the receiver measured signal to noise density ratio (c/no)outputs, and

[0016] ii) varying the rate of response of the Kalman filter tomeasurements from the satellite navigation system in response to changesin the tracking loop bandwidths such that correlated measurement noisein the Kalman filter is avoided.

[0017] It should be noted that the bandwidths of the tracking loops fordifferent satellites are likely to vary independently of one another,particularly where a controlled radiation pattern antenna (CRPA) isused. Therefore, the adaptive inertia/satellite navigation systemintegration algorithm should be capable of adapting the Kalman filterfor each tracking loop.

[0018] Where the tracking loop bandwidths are not a direct output of thesatellite receiver they may be inferred from the receiver measuredsignal to noise density ratio (c/n₀). The variation of the tracking loopbandwidth with measured (c/n₀) is different for each receiver design. Itis therefore necessary either to obtain the information from themanufacturer or to infer it from laboratory testing of the receiverusing a GPS signal simulator capable of generating interference.

[0019] By adapting the Kalman filter to the tracking loop bandwidth thebest use of the satellite data is made. There are a number of ways inwhich the filter can be adapted.

[0020] The, update interval (iteration rate) of the Kalman filter can bevaried. Below a threshold bandwidth the interval between measurementupdates from each tracking channel is varied in inverse proportion tothe tracking channel bandwidth. Therefore for low bandwidths theiteration rate of the filter can be reduced. As an alternative to thisthe measurement data can be averaged over the iteration intervalprovided the averaged measurement is treated as a single measurement forstatistical purposes.

[0021] Alternatively, the Kalman gain matrix can be weighted down inorder to obtain a rate of response of Kalman filter estimates tomeasurements equivalent to that obtained by increasing the measurementupdate interval. In this variation of the invention the measurementupdate interval remains fixed for each measurement type—pseudo-range andpseudo range-rate. When the tracking loop bandwidth drops below athreshold value, to which the update interval is tuned, the Kalman gainmatrix is weighted down to simulate increasing the measurement updateinterval.

[0022] The weighting of the Kalman gain matrix can conveniently beachieved by multiplying it by the time between successive (correlated)measurements divided by the time between successive un-correlatedmeasurements.

[0023] Weighting of the gain matrix can also be achieved by multiplyingit by a suitable adaption matrix. If the Kalman gain matrix isrepresented as one n_(t) column matrix for pseudo-range measurements anda second n_(t) column matrix for pseudo-range rate measurements, wheren_(t) is the number of satellites tracked, then each adaption matric Ais an n_(t)×n_(t) diagonal matric wherein

[0024] i) for the elements of the pseudo-range adaption matrix A_(pkii)= 1 for B_(L) _(—) _(COi) ≧ B_(L) _(—) _(COT) A_(pkii) = B_(L) _(—)_(COi)/B_(L) _(—) _(COT) for B_(L) _(—) _(COi) < B_(L) _(—) _(COT)A_(pkij) = 0   i ≠ j

[0025]  where B_(L) _(—) _(COi) is the code tracking bandwidth oftracking channel i and B_(L) _(—) _(COT) is the threshold code trackingbandwidth for adaption, and;

[0026] ii) for the elements of the pseudo-range rate adaption matrixA_(rkii) = 1 for B_(L) _(—) _(CAi) ≧ B_(L) _(—) _(CAT) A_(rkii) = B_(L)_(—) _(CAi)/B_(L) _(—) _(CAT) for B_(L) _(—) _(CAI) < B_(L) _(—) _(CAT)A_(rkij) = 0   i ≠ j

[0027]  where B_(L) _(—) _(CAi) is the carrier tracking bandwidth oftracking channel i and B_(L) _(—) _(CAT) is the threshold carriertracking bandwidth for adaption.

[0028] A further way of adapting the Kalman filter is to vary themeasurement noise covariance, R, which is a quantity that is variedwithin the Kalman gain matrix. Either this can be done by multiplying itby the time between successive un-correlated measurements divided by thetime between successive (correlated) measurements or by dividing by anadaption matrix analogous to that described above. In the latter case,this involves replacing R within the Kalman gain matrix, K_(k) with R′where R′=R/A

[0029] An additional way of adapting the Kalman filter is to model thetime correlated measurement noise explicitly, either as additionalKalman filter states or as correlated measurement noise using aSchmidt-Kalman filter with Uncertain parameters (for more information onthe Schmidt-Kalman filter algorithm see Stochastic Processes andFiltering Theory by Andrew H. Jazwinski, Academic Press (1970)). Ineither case, the correlated measurement noise estimate, {circumflex over(x)}, is modelled as a first order Markov process, i.e.${\frac{\hat{x}}{t} = {- \frac{\hat{x}}{\tau_{c}}}},$

[0030] where the correlation time, τ_(c), should be modelled asinversely proportional to the tracking loop bandwidths.

[0031] An embodiment of the adaptive method of integrating INS andsatellite-radio navigation data according to the present invention willnow be described with reference to FIG. 1 which depicts an adaptivetightly-coupled INS/GPS integrated navigation system.

[0032] Turning to FIG. 1, a tightly coupled INS/GPS integratednavigation system is shown. A GPS receiver 1 is connected to a Kalmanfilter 3. An INS 5 is connected to the Kalman filter 3 and also the GPSreceiver 1. A Kalman gain re-weighting function 9 is connected to boththe Kalman filter 3 and the GPS receiver 1.

[0033] In use, the GPS receiver 1 outputs pseudo-range and pseudo-rangerate measurements 2 to the Kalman filter 3. It is assumed that thesepseudo-range and pseudo-range rate measurements have been combined fromthe individual L1 and L2 frequency measurements to correct forionosphere propagation delays. The receiver 1 also sends GPS broadcastnavigation data 4 to the Kalman filter 3, which enables the satellitepositions, velocities and clock offsets to be calculated.

[0034] The INS 5 outputs position, velocity and attitude 6 measurementsto the Kalman filter 3. The Kalman filter 3 (in a closed-looparchitecture) sends corrections 7 back to the INS 5. These correctionscomprise Kalman filter estimates of the INS position, velocity, attitudeand inertial instrument errors. The INS 5 uses these to correct itsposition, velocity and attitude solution and to correct the outputs ofits constituent inertial sensors. INS position, velocity and attitude 8outputs are also sent to the GPS receiver 1, which uses them to aid thecode tracking loops of those satellite signals for which carriertracking cannot be implemented due to low signal to noise ratios.

[0035] The Kalman filter 3 comprises a standard tightly-coupled INS/GPSintegration algorithm, with the exception that the Kalman gain, K, isre-weighted. The Kalman filter operates a standard system propagation(or prediction) cycle. It operates a standard measurement update cycleup to and including the calculation of the Kalman gain matrices. AKalman gain re-weighting function 9 takes unweighted Kalman gainmatrices 10 computed by the Kalman filter for the current set ofpseudo-range measurements and the current set of pseudo-range ratemeasurements and multiplies weighted Kalman gain matrices 11 which aresent to the Kalman filter. The Kalman filter 3 then resumes themeasurement update cycle using the re-weighted Kalman gain matrices.

[0036] The Kalman gain re-weighting function 9 calculates the adaptationmatrices, A, using the formulae presented above from the tracking loopbandwidths 12 output by the GPS receiver 1. Where the GPS receiver doesnot output tracking loop bandwidths, an empirical model is insertedbetween 1 and 9 to estimate the bandwidths 12 as a function of thereceiver output (c/n₀) measurements.

1. A method of integrating inertial navigation system and satellitenavigation system data in a tightly coupled architecture by means of aKalman filter, the satellite navigation data being received on areceiver having adaptive tracking loop bandwidths, comprising i)monitoring the tracking loop bandwidths or modelling them as a functionof the receiver measured signal to noise density ratio (c/n₀) outputs,and ii) varying the rate of response of the Kalman filter tomeasurements from the satellite navigation system in response to changesin the tracking loop bandwidths such that correlated measurement noisein the Kalman filter is avoided.
 2. A method as claimed in claim 1wherein the Kalman filter is varied for each tracking loop.
 3. A methodas claimed in any preceding claim wherein the tracking loop band widthsare calculated from the received signal to noise density ratio.
 4. Amethod as claimed in any preceding claim wherein the iteration rate ofthe Kalman filter is varied in inverse proportion to the tracking loopbandwidth.
 5. A method as claimed in any preceding claim whereinmeasurement data averaged is averaged over the iteration period.
 6. Amethod as claimed any of claims 1 to 3 wherein the Kalman gain matrix isweighted by multiplying it by the time between successive measurementsdivided by the time between successive uncorrelated measurements.
 7. Amethod as claimed in any of claims 1 to 3 wherein the Kalman gain matrixis represented as one n_(t) column matrix for pseudo-range measurementsand a second n_(t) column matrix for pseudo-range rate measurements,where n_(t) is the number of satellites tracked, and is then weighted byan adaption matrix A, the adaption matrix being an n_(t)×n_(t) diagonalmatrix where i) the elements of the pseudo-range adaption matrix areA_(pkjj) = 1 for B_(L) _(—) _(COi) ≧ B_(L) _(—) _(COT) A_(pkii) = B_(L)_(—) _(COi)/B_(L) _(—) _(COT) for B_(L) _(—) _(COi) < B_(L) _(—) _(COT)A_(pkij) = 0   i ≠ j

 where B_(L) _(—) _(COi) is the code tracking bandwidth of trackingchannel i and B_(L) _(—) _(COT) is the threshold code tracking bandwidthfor adaption, and; ii) the elements of the pseudo-range rate adaptionmatrix are A_(rkii) = 1 for B_(L) _(—) _(CAi) ≧ B_(L) _(—) _(CAT)A_(rkii) = B_(L) _(—) _(CAi)/B_(L) _(—) _(CAT) for B_(L) _(—) _(CAi) <B_(L) _(—) _(CAT) A_(rkij) = 0   i ≠ j

 where B_(L) _(—) _(CAi) is the carrier tracking bandwidth of trackingchannel i and B_(L) _(—) _(CAT) is the threshold carrier trackingbandwidth for adaption.
 7. A method as claimed in any of claims 1 to 3wherein the measurement noise covariance, R, is divided by an adaptionmatrix A as claimed in claim
 6. 8. A method as claimed in any of claims1 to 3 wherein the measurement noise covariance, R, is weighted bymultiplying by the time between successive uncorrelated measurementsdivided by the time between successive measurements.
 9. A method asclaimed in any preceding claim wherein the satellite navigation systemis a Global Positioning System.
 10. A method of integrating inertialnavigation system and satellite navigation system data in a tightlycoupled architecture by means of a Kalman filter, the satellitenavigation data being received on a receiver having adaptive trackingloop bandwidths, comprising i) monitoring the tracking loop bandwidthsor modelling them as a function of the receiver measured signal to noisedensity ratio (c/n₀) outputs, and ii) modelling the correlatedmeasurement noise within the Kalman filter explicitly such that theassumed correlation time is varied in inverse proportion to the trackingloop bandwidths.
 11. A method as claimed in claim 10 wherein thecorrelation time is varied independently for measurements from eachtracking loop.
 12. A method as claimed in claim 10 wherein the trackingloop bandwidths are calculated from the received signal to noise densityratio.
 13. A method as claimed in claims 10 to 12 wherein the correlatedmeasurement noise is estimated as Kalman filter states.
 14. A method asclaimed in claims 10 to 12 wherein the correlated measurement noise ismodelled using a Schmidt-Kalman filter algorithm.